On the leading OPE corrections to the ghost-gluon vertex and the Taylor theorem

This brief note is devoted to a study of genuine non-perturbative corrections to the Landau gauge ghost-gluon vertex in terms of the non-vanishing dimension-two gluon condensate. We pay special attention to the kinematical limit which the bare vertex takes for its tree-level expression at any perturbative order, according to the well-known Taylor theorem. Based on our OPE analysis, we also present a simple model for the vertex, in acceptable agreement with lattice data.Comment: Final version published in JHE

The strong coupling constant at small momentum as an instanton detector

We present a study of $\alpha_{MOM}(p)$ at small p computed from the lattice. It shows a dramatic $\propto p^4$ law which can be understood within an instanton liquid model. In this framework the prefactor gives a direct measure of the instanton density in thermalised configurations. A preliminary result for this density is 5.27(4) fm^{-4}.Comment: 12 pages, 4 figure

Testing Landau gauge OPE on the Lattice with a <A2><A^2> Condensate

Using the operator product expansion we show that the $O(1/p^2)$ correction to the perturbative expressions for the gluon propagator and the strong coupling constant resulting from lattice simulations in the Landau gauge are due to a non-vanishing vacuum expectation value of the operator $A^\mu A_\mu$. This is done using the recently published Wilson coefficients of the identity operator computed to third order, and the subdominant Wilson coefficient computed in this paper to the leading logarithm. As a test of the applicability of OPE we compare the $$ estimated from the gluon propagator and the one from the coupling constant in the flavourless case. Both agree within the statistical uncertainty: $\sqrt{} \simeq 1.64(15)$ GeV. Simultaneously we fit \Lams = 233(28) MeV in perfect agreement with previous lattice estimates. When the leading coefficients are only expanded to two loops, the two estimates of the condensate differ drastically. As a consequence we insist that OPE can be applied in predicting physical quantities only if the Wilson coefficients are computed to a high enough perturbative order.Comment: 15 pages, LaTex file with 5 figure

The anomalous dimension of the gluon-ghost mass operator in Yang-Mills theory

The local composite gluon-ghost operator $({1/2}A^{a\mu}A_{\mu}^{a}+\alpha \bar{c}^{a}c^{a})$ is analysed in the framework of the algebraic renormalization in SU(N) Yang-Mills theories in the Landau, Curci-Ferrari and maximal abelian gauges. We show, to all orders of perturbation theory, that this operator is multiplicatively renormalizable. Furthermore, its anomalous dimension is not an independent parameter of the theory, being given by a general expression valid in all these gauges. We also verify the relations we obtain for the operator anomalous dimensions by explicit 3-loop calculations in the MSbar scheme for the Curci-Ferrari gauge.Comment: 12 pages, LaTeX, final version to appear in Phys. Lett.

Preliminary Calculation of αs\alpha_s from Green Functions with Dynamical Quarks

We present preliminary results on the computation of the QCD running coupling constant in the $\widetilde{MOM}$ scheme and Landau gauge with two flavours of dynamical Wilson quarks. Gluon momenta range up to about 7 GeV ($\beta =$ 5.6, 5.8 and 6.0) with a constant dynamical-quark mass. This range already allows to exhibit some evidence for a sizable $1/\mu^2$ correction to the asymptotic behaviour, as in the quenched approximation, although a fit without power corrections is still possible with a reasonable $\chi^2$. Following the conclusions of our quenched study, we take into account $1/\mu^2$ correction to the asymptotic behaviour. We find $\Lambda_{\rm \bar{MS}}^{N_f=2} = 264(27) {\rm MeV} \times [{a^{-1}(5.6,0.1560)}/{2.19 {\rm GeV}}]$, which leads to $\alpha_s(M_Z) = 0.113(3)(4)$. The latter result has to be taken as a preliminary indication rather than a real prediction in view of the systematic errors still to be controlled. Still, being two sigmas below the experimental result makes it very encouraging.Comment: 14 pages, 3 figs., 2 tabs., revte

Remarks on the determination of the Landau gauge OPE for the Asymmetric three gluon vertex

We compute a compact OPE formula describing power corrections to the perturbative expression for the asymmetric $\widetilde{MOM}$-renormalized running coupling constant up to the leading logarithm. By the use of the phenomelogical hypothesis leading to the factorization of the condensates through a perturbative vacuum insertion, the only relevant condensate in the game is $$. The validity of the OPE formula is tested by searching for a good-quality coherent description of previous lattice evaluations of $\widetilde{MOM}$-renormalized gluon propagator and running coupling.Comment: 12 pages, 3 figures (2 generated by the macro: axodraw.sty

Instantons and <A2><A^2> Condensate

We argue that the $$condensate found in the Landau gauge on lattices, when an Operator Product Expansion of Green functions is performed, might be explained by instantons. We use cooling to estimate the instanton contribution and extrapolate back the result to the thermalised configuration. The resulting$$ is similar to $$.Comment: 6 pages, 1 fig., 1 tab., RevTeX to be use

Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.Comment: 20 pages, no figure

Masses and Decay Constants of Heavy-Light Mesons Using the Multistate Smearing Technique

We present results for f_B and masses of low-lying heavy-light mesons. Calculations were performed in the quenched approximation using multistate smearing functions generated from a spinless relativistic quark model Hamiltonian. Beta values range from 5.7 to 6.3, and light quark masses corresponding to pion masses as low as 300 MeV are computed at each value. We use the 1P--1S charmonium splitting to set the overall scale.Comment: 9 pages, 13 figures, and 5 tables as a single 193K compressed and uuencoded Postscript file, FERMILAB--CONF--93/376-

Gauge invariance of dimension two condensate in Yang-Mills theory

Gauge independence of dimension two condensate in Yang-Mills theory is demonstrated by using a noncommutative theory technique.Comment: 7 page